Scroll down on that great page (part of the most comprehensive composting site I know of) for the info on weeds/weed seeds, which includes this advice about bagging (to solarize/cook to death) the unwanted weeds, BEFORE adding them to the heap:

“Some perennial weeds will be killed in a hot heap; avoid really persistent horrors such as celandine, docks, bulbous buttercup, ground elder and bindweed. Don’t burn or dump these weeds – they are rich in plant foods. Mix with grass mowings in a plastic sack. Tie it up and leave for a few months until the weeds are no longer recognisable, then add to the compost heap. Or send them to your local council green waste recycling facility where the composting methods are hot enough to kill them off.”

The bagging idea is great — a sort of waste not, want not tactic for recycling them versus tossing them into the trash — and you can use a few bags over and again. The weeds I bag instead of adding right to the heap include any with strong runners (like goutweed, or former garden plants I now find too ambitious like plume poppy or ajuga) and any that have started to flower before I pulled them.

P.S. — More on weeds (particularly on ID’ing them so you know what you are up against) in this blog post: